基于SDRE具有终端碰撞角约束的非线性微分对策制导律

通过非线性微分对策理论讨论了具有终端碰撞角约束的弹目追逃问题,提出了基于求解状态相关黎卡提方程(state dependent Riccati equation,SDRE)的方法解决该微分对策问题,得到了具有终端碰撞角约束的SDRE解析解。提出的终端碰撞角约束制导律是以弹目视线角速率及碰撞角误差为状态向量进行推导,并研究了闭环系统局部渐进稳定的条件。该制导律不需要进行剩余时间的预测。最后针对目标不进行机动、进行阶跃机动、正弦机动及目标最优机动形式4种情况,进行了制导律的仿真验证,仿真结果表明该制导律对于不同机动目标均具有良好的制导效果且能很好地满足末端碰撞角约束要求。

Nonlinear differential games guidance law based on SDRE with terminal impact angular

The problem of intercepting a maneuvering target at a terminal impact angular is discussed in the nonlinear differential games framework. A feedback form solution is proposed by extending the state dependent Riccati equation (SDRE) method to nonlinear zero sum differential games. An analytic solution is obtained for the SDRE corresponding to the impact angle constrained guidance problem. The impact angle constrained guidance law is derived using the line-of-sight rate and projected terminal impact angle error as the state vectors. Local asymptotic stability conditions for the closed loop system corresponding to these states are studied. Time to go estimation is not explicitly required to derive and implement the proposed guidance law. Finally, through mathematical simulations, the derived guidance law is tested under four scenarios of target maneuvering: nonmaneuvering, step maneuvering, sine maneuvering and the best control maneuvering. The simulation results show that the guidance law have good effects for different maneuvering targets and can satisfy terminal impact angular constraint requirements.